TASK: What is a ratio? Provide an example and your explanation. (Look back at your flashcards if you need a hint)
TASK: What is a proportion? Provide an example along with your explanation. (Look back at your flashcards if you need a hint).
How do we set up proportions?
Proportions are 2 ratios that are equal to each other. Ratios are fractions that are comparing two different units (This should sound familiar from when we learned about rate. Rate is a ratio because we are comparing two units. The difference is that with rate we then divide the ratio). When we are setting up a proportion, it always looks that same. We have two ratios (fractions) with an equals sign in between them.
The most important thing about a proportion is that whatever units are in the numerator of the first ratio are also in the numerator of the second ratio. Also, whatever units are in the denominator of the first ratio are the same as the units in the denominator of the second ratio. The actual numbers can (and should) be different, but the UNITS must be THE SAME. For example we can have:
or
but we CANNOT have:
or
TASK: How do we set up proportions? What do they look like? What do they NOT look like?
How do we use proportions?
On the Regents, we will use proportions in 2 ways. The first way will be when working with rate. The other way will be when solving equations.
Most of the time, problems that use proportions will be WORD PROBLEMS. We can recognize when a word problem is asking us to use a proportion when they give us the rate in the problem OR when they give us two units to compare in two different situations. Take a look at this example:
In this problem, we are comparing MILES and HOURS in two situations. In one situation, we have 275 miles and 5.25 hours. In the other situations we have 1 hour and an unknown number of miles. This means that we can set up a proportion that is comparing miles and hours.
We can substitute the numbers from the problem into the proportion. The numbers from one situation will go in one ratio and the numbers from the other situation will be in the other ratio (we can't switch them around). We'll use a variable to represent the unknown number of miles. So we get:
TASK: How can we identify a problem that is asking us to use proportions?
TASK: How do we set up the proportion from a word problem?
TASK: Set up a proportion that could be used to solve each of the following problems:
TASK: What is a proportion? Provide an example along with your explanation. (Look back at your flashcards if you need a hint).
How do we set up proportions?
Proportions are 2 ratios that are equal to each other. Ratios are fractions that are comparing two different units (This should sound familiar from when we learned about rate. Rate is a ratio because we are comparing two units. The difference is that with rate we then divide the ratio). When we are setting up a proportion, it always looks that same. We have two ratios (fractions) with an equals sign in between them.
The most important thing about a proportion is that whatever units are in the numerator of the first ratio are also in the numerator of the second ratio. Also, whatever units are in the denominator of the first ratio are the same as the units in the denominator of the second ratio. The actual numbers can (and should) be different, but the UNITS must be THE SAME. For example we can have:
or
but we CANNOT have:
or
TASK: How do we set up proportions? What do they look like? What do they NOT look like?
How do we use proportions?
On the Regents, we will use proportions in 2 ways. The first way will be when working with rate. The other way will be when solving equations.
Most of the time, problems that use proportions will be WORD PROBLEMS. We can recognize when a word problem is asking us to use a proportion when they give us the rate in the problem OR when they give us two units to compare in two different situations. Take a look at this example:
In this problem, we are comparing MILES and HOURS in two situations. In one situation, we have 275 miles and 5.25 hours. In the other situations we have 1 hour and an unknown number of miles. This means that we can set up a proportion that is comparing miles and hours.
We can substitute the numbers from the problem into the proportion. The numbers from one situation will go in one ratio and the numbers from the other situation will be in the other ratio (we can't switch them around). We'll use a variable to represent the unknown number of miles. So we get:
TASK: How can we identify a problem that is asking us to use proportions?
TASK: How do we set up the proportion from a word problem?
TASK: Set up a proportion that could be used to solve each of the following problems:
1.
2.
3.